Given $ m \angle ABC = 6x + 44$, and $ m \angle CBD = 8x + 52$, find $m\angle CBD$. $B$ $A$ $D$ $C$
Answer: From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Since $\angle ABD$ is a straight angle, we know ${m\angle ABD = 180}$ Substitute in the expressions that were given for each measure: $ {6x + 44} + {8x + 52} = {180}$ Combine like terms: $ 14x + 96 = 180$ Subtract $96$ from both sides: $ 14x = 84$ Divide both sides by $14$ to find $x$ $ x = 6$ Substitute $6$ for $x$ in the expression that was given for $m\angle CBD$ $ m\angle CBD = 8({6}) + 52$ Simplify: $ {m\angle CBD = 48 + 52}$ So ${m\angle CBD = 100}$.